I have an RN-42 Bluetooth Mate Silver module hooked up to my Arduino Uno. I'd like to solder a wire to the green "Connected" LED on the Bluetooth module, connect the wire to my Arduino to allow me to "sense" when the LED is illuminated.

Any suggestions on how to do this?

Here's the link for the schematic (PDF) for the RN-42 Bluetooth Mate Silver module. The Green LED is indicated on the right side of the drawing:

Just be careful not to accidentally drive 5V into that signal - you could add a 10k resistor in series to prevent that possibility.

[ oh, and one caveat, its possible that the bluetooth module doesn't drive that signal high enough (due to the current load from the LED) - it needs to be 3.0V or more to guarantee working with the Arduino input - you can measure this voltage when the LED is on to double check this ]

Just adc the voltage on that 330ohm resistor - it gives you the current.

Now, that is highly simplistic: it assumes that if you sense a current on that resistor, there is current going through it (to ground). It is entirely possible that there is an open circuit so there is voltage on the resistor but no current going through it. You can software detect that.

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to "sense" when the LED is illuminated.

That is actually quite different from sensing the current: you can have current going through an LED yet it is not illuminating.

If you really want to sense illumination, use a light sensor (photoresistor / diode / transistor for example).